User:Aravind V R/sandbox1/Number

Number theory
Fields	Algebraic number theory (class field theory, non-abelian class field theory, Iwasawa theory, Iwasawa–Tate theory, Kummer theory) Analytic number theory (analytic theory of L-functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry (Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics (additive number theory) Arithmetic geometry (anabelian geometry, p-adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers 0 Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers p-adic numbers (p-adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Irrationality measure Simple continued fractions
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Notes

Euclid's algorithm Euclid's lemma Twin prime Prime number theorem Mobius function Dirichlet product Heron triangle Reduced residue system

Fermat theorem Wilson's theorem Quadratic residue modulo p Euler's criterion Gauss's lemma Fermat's little theorem Legendre symbol Jacobi symbol

Quadratic residue Square and multiply algorithm

Arithmetic functions

• Möbius function
• Euler's totient function
• Liouville function
• Von Mangoldt function